Galaxy and Mass Assembly (GAMA) is a project to study galaxy formation and evolution, combining imaging data from ultraviolet to radio with spectroscopic data from the AAOmega spectrograph on the Anglo-Australian Telescope. Using data from Phase 1 of GAMA, taken over three observing seasons, and correcting for various minor sources of incompleteness, we calculate galaxy luminosity functions (LFs) and their evolution in the ugriz passbands. At low redshift, z < 0.1, we find that blue galaxies, defined according to a magnitude-dependent but non-evolving colour cut, are reasonably well fitted over a range of more than 10 magnitudes by simple Schechter functions in all bands. Red galaxies, and the combined blue plus red sample, require double power-law Schechter functions to fit a dip in their LF faintwards of the characteristic magnitude M* before a steepening faint end. This upturn is at least partly due to dust-reddened disc galaxies. We measure the evolution of the galaxy LF over the redshift range 0.002 < z < 0.5 both by using a parametric fit and by measuring binned LFs in redshift slices. The characteristic luminosity L* is found to increase with redshift in all bands, with red galaxies showing stronger luminosity evolution than blue galaxies. The comoving number density of blue galaxies increases with redshift, while that of red galaxies decreases, consistent with prevailing movement from blue cloud to red sequence. As well as being more numerous at higher redshift, blue galaxies also dominate the overall luminosity density beyond redshifts z≃ 0.2. At lower redshifts, the luminosity density is dominated by red galaxies in the riz bands, and by blue galaxies in u and g